What shape is the universe

[batmanmg]

well?

im convinced that the universe is in fact a 4d shell. your not going to convince me otherwise. if you bend the 3rd dimension, it must be bent 4th dimensionaly. so the curvature of the universe must conclude that it has a 4d shape.

well maybe you can convince me otherwise.

but still an answer to the quesiton would be nice.

What 4d shape is the universe a shell of?

i'd like to think that its an egg shaped glome. (but thats becuase i have no clue)

[wendy]

It is true that the present 3d space is curved, but this curvature does not happen because the shape is bent in a higher dimension. It does not even have to be a shape of anything in particular.

If it were the covering of some 4d solid, then the model of the universe would be spheric. That is, there is positive curvature, and as circles get bigger, the circumference is less than 2.pi.r.

There was some talk of the "poincare dodecahedron". This is a repetition of the same shape, say a pentagonal dodecahedron, or a pentagonal tegum, 120 times over the surface of a 4-sphere. However, this idea has fallen out of favour.

In practice, the observed curvature over great distances is very close to zero. This equates in hyperbolic space, to a proper curve called a horosphere.

However, the existance of "curvature" in space does not equate to the existance of a higher dimension. All space is curved, and therefore the embedding space ought be curved in something higher as well!

What happens with curvature, is this. Imagine you have something like a cloth. For some point in the cloth, you can draw out some 360 degrees. A circle of radius 57.3 mm in euclidean geometry would make a circle of 360 mms circumference.

Imagine that instead of each degree being equal, it is possible for degrees to be variable lengths. So this degree is 1.010 m/m, while the next is 1.009 m/m.

The model of gravity as a curvature of space is that this space is in tension. If one half of the circle is longer than the other half, it pulls harder, and the object at rest at the centre moves to the side of higher tension.

The various horn-shaped pits you see in relativity diagrams make the parts of the circle that lie in the hole longer than the bit that lies outside of it, and things tend to move into the direction of longer side: ie the hole side.

W

[batmanmg]

However, the existance of "curvature" in space does not equate to the existance of a higher dimension. All space is curved, and therefore the embedding space ought be curved in something higher as well!

i disagree. a dimension cannot be curved. space can be curved, and all of its rules then abide by this curve. but the dimension itself must remain ridgid.

there is our curved universe and there is a paralel universe whose space isn't curved. If you overlapped the two universes, it would be like overlapping a flat peice of paper with a spherical shell. one has to be curved in a higher dimension.

In practice, the observed curvature over great distances is very close to zero. This equates in hyperbolic space, to a proper curve called a horosphere.

the same observation was made about the earth. its one reason ppl thoguht it was flat. Its a sphere though. so why not our universe?


im wondering if we are talking about the same curvature. mostly im talking about the odd expansions of the universe. i heard the analogy that its like being points on a balloon. and the baloon is gettin blown up, so all the points are moving away from every other point. but i think that the idea can be applied to curvatures due to gravity, and the like. just not to effect the overal shape, only to deviate from it. thats why i chose and egg shape.

[moonlord]

A dimension can be curved, unlike the others in a space. Take for example S1xE1 - the cylindrical surface. Only one of the two directions is curved.

[batmanmg]

I thought that a dimension was a mathmatical concept and not a physical one. if one looks at a non euclidan plain they give it a shape regardless. saddle, spherical, parabolic, not sure really what all of them are or if i named too many. if the 3d dimension is warped it must be warped 4th dimensionaly as compared to euclidian geomitry. my question is what is this shape?

[PWrong]

Well the universe looks flat on average, so it probably is. If it was a glome it would have curvature. But it also doesn't have a centre or anything. So my guess is the flat tri-torus. That is, the 3D surface of the 6D rotatope 222.

[batmanmg]

im still very new to rotatopes and the like. so I can only say... HUH? any jump off point you'd suggest to looking into the subject?

also, is this conducive to the idea that if you travle in any given direction in the universe and keep going, you'll end up where you started? or is this idea not valid. Its the flat part that threw me off.

[PWrong]

Well, if the universe was 2D and wraps around, you could say it was the surface of a torus. But the torus is curved. The margin of a duocylinder is similar to a torus, except flat. The 3D equivalent of the duocylinder is the flat 3-torus, which has to sit in 6 dimensions.

also, is this conducive to the idea that if you travle in any given direction in the universe and keep going, you'll end up where you started?

That's right.

Its the flat part that threw me off.

Essentially, flat means that parallel lines exist. Note that on a sphere, there are no parallel lines (A line is a great circle, like the equator or a meridian. Lines of longitude don't count as straight lines). Any two lines will eventually meet. The surface of a glome has the same problem. I think the torus doesn't, but it has other curvature problems. I could be wrong about this.

[thigle]

... my guess is the flat tri-torus. That is, the 3D surface of the 6D rotatope 222.

does this have anything to do with the fact that the manifold of all the rotations around a 3-point is a 6-point ? (or it seems to me to be so?)

idea that in any given direction in the universe and keep going, you'll end up where you started...

that's right

what conditions must the kind of space in which this is true fulfill ?
i just know that in order to come back revesed from such a trip, the space must be multiply connected and if projective, than of odd dimensionality ? is that so ? can someone comment on it or fix it ?

[batmanmg]

well what i meant when i asked was weither it was circle pathed. when you end up at the same position your not reversed or anything. just went around in a big loop.

what shape do you think the universe is? (for those who skipped to the most recent post, keep in mind the properties of the expansion of the universe)

[Nick]

According to Stephen Hawking, time is pear shaped. That's part of the universe.

[papernuke]

calibi-yau shapes are the curled up "other" dimensions, then shouldnt we that shape?

[houserichichi]

No, Calabi-Yaus are theorized to exist at all points in spacetime (even that I'm unsure - I suspect that may all be outdated) but spacetime itself is not that shape. String theory also has no evidence, btw.

[batmanmg]

but the expansion of the universe does... any other ideas?